Universality Limits, Orthogonal Polynomials and Weighted Polynomial Approximation

我们提出了一种证明正交多项式通用性极限的新方法。例如，我们允许权重全局为正a.e.，并且在给定点连续。这对于一个固定权值的通用性来说就足够了。我们打算探索这种方法对于紧集和非紧集上的权值，以及对于变权值的限制。这种类型的普适性极限出现在随机矩阵理论及其应用中，涉及数学物理的各个领域。重要的是，需要先前强有力的全局假设，例如分析性。现在只需要薄弱的局部和全球假设。

We have developed a new approach to proving universality limits involving orthogonal polynomials. We allow, for example, the weight to be positive a.e. globally, and continuous at a given point. That is enough for universality for a fixed weight. We intend to explore the limits of this method for weights on compact and non-compact sets, as well as for varying weights.Universality limits of this type arise in the theory of random matrices and its applications, which include various topics in mathematical physics. The significance is that previously strong global hypotheses were required, such as analyticity. Now only weak local and global assumptions are required.